Being Asked To Serve Notice Period On The Basis Of An Offer Letter

Dear Seniors ,

I was given an offer letter by a company but the location was not suitable to me . After discussion over phone they agreed to give the location that I wanted . Thus I joined them .
After 4 days they asked me that I will have to travel to different locations and I did not like the culture of the company and neither my role , so I just sent a two line email stating that I will not be continuing with them.
They did not issue me any appointment letter and I was working on an offer letter . Even the company ID card was not issued to me .
Now the head of talent acquisition send me a SMS that I need to serve the notice period for 1 month.
I told him that I don't have any document stating that . He said he wanted to give me the appointment letter but since I did not work he was not able to give it to me .
He told me that since the company bought a desktop for me , I have to pay the one month notice period .

Please help me in this as I don't want to be harassed by this company

Since you've made up your mind once for all not to continue with the Company, better pay the notice salary and make your exit smooth and cordial.

Dear ,
You don't need to be worried.
Normally offer letter doesn't carry any legal T&Cs and as you didn't sign any appointment letter you are not liable to fulfil any T&Cs imposed by them on you subject to you didn't sign any other documents relating to your retention in the company. So don't worry about the phone calls. They can't do anything.
Also note, leaving a company in a short period of time is not at all appreciable. If you didn't like the company's culture and the job location or profile then you could have sat with them and discuss about the issues. Writing a mail from home without discussing the matter with them is not good. Remember whenever you leave any job , maintain good relationship with the employer because you never know this employer may turn out to be of some help for you in future.